401-3830-69L  Seminar on Minimal Surfaces

SemesterAutumn Semester 2019
LecturersA. Carlotto
Periodicitynon-recurring course
Language of instructionEnglish
CommentThe total number of students who may take this course for credit is limited to twenty; however further students are welcome to attend.


401-3830-69 SSeminar on Minimal Surfaces28s hrs
Mon/2w16:15-18:00HG G 26.3 »
Tue/2w15:15-17:00HG G 26.1 »
16.12.16:15-18:00HG G 19.2 »
17.12.15:15-17:00HG G 26.1 »
A. Carlotto

Catalogue data

AbstractThis course is meant as an invitation to some key ideas and techniques in Geometric Analysis, with special emphasis on the theory of minimal surfaces. It is primarily conceived for advanced Bachelor or beginning Master students.
ObjectiveThe goal of this course is to get a first introduction to minimal surfaces both in the Euclidean space and in Riemannian manifolds, and to see analytic tools in action to solve natural geometric problems.

Students are guided through different types of references (standard monographs, surveys, research articles), encouraged to compare them and to critically prepare some expository work on a chosen topic.

This course takes the form of a working group, where interactions among students, and between students and instructor are especially encouraged.
ContentThe minimal surface equation, examples and basic questions. Parametrized surfaces, first variation of the area functional, different characterizations of minimality. The Gauss map, basic properties. The Douglas-Rado approach, basic existence results for the Plateau problem. Monotonicity formulae and applications, including the Farey-Milnor theorem on knotted curves.
The second variation formula, stability and Morse index. The Bernstein problem and its solution in the two-dimensional case. Total curvature, curvature estimates and compactness theorems. Classification results for minimal surfaces of low Morse index.
LiteratureThree basic references that we will mostly refer to are the following ones:

1) B. White, Lectures on minimal surface theory, Geometric analysis, 387–438, IAS/Park City Math. Ser., 22, Amer. Math. Soc., Providence, RI, 2016.

2) T. Colding, W. Minicozzi, A course in minimal surfaces. Graduate Studies in Mathematics, 121. American Mathematical Society, Providence, RI, 2011. xii+313 pp.

3) R. Osserman, A survey of minimal surfaces. Second edition. Dover Publications, Inc., New York, 1986. vi+207 pp.

Further, more specific references will be listed during the first two introductory lectures.
Prerequisites / NoticeThe content of the first two years of the Bachelor program in Mathematics, in particular all courses in Real and Complex Analysis, Measure Theory, Topology.

Some familiarity with the language of Differential Geometry, although not a formal pre-requisite, might be highly helpful. Finally, a first course on elliptic equations (especially on basic topics like Schauder estimates and the maximum principle) might also be a plus.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits4 credits
ExaminersA. Carlotto
Typeungraded semester performance
Language of examinationEnglish
RepetitionRepetition only possible after re-enrolling for the course unit.

Learning materials

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No information on groups available.


Places20 at the most
PriorityRegistration for the course unit is only possible for the primary target group
Primary target groupMathematics BSc (404000) starting semester 05
Mathematics MSc (437000)
Applied Mathematics MSc (437100)
Mathematics (Mobility) (448000)
Waiting listuntil 30.09.2019

Offered in

Mathematics BachelorSeminarsWInformation
Mathematics MasterSeminarsWInformation